# ginzburg_neuron – Binary stochastic neuron with sigmoidal activation function¶

## Description¶

The `ginzburg_neuron`

is an implementation of a binary neuron that
is irregularly updated as Poisson time points. At each update
point, the total synaptic input h into the neuron is summed up,
passed through a gain function g whose output is interpreted as
the probability of the neuron to be in the active (1) state.

The gain function used here is \(g(h) = c_1 h + c_2 (1 + \tanh(c_3 (h-\theta)))/2\) (output clipped to \([0, 1]\)). This permits affine-linear (\(c_1\neq0, c_2\neq0, c_3=0\)) or sigmoidally shaped (\(c_1=0, c_2=1, c_3\neq0\)) gain functions. The latter choice corresponds to the definition in 1, giving the name to this neuron model.

The choice \(c_1=0, c_2=1, c_3=\beta/2\) corresponds to the Glauber dynamics 2, \(g(h) = 1 / (1 + \exp(-\beta (h-\theta)))\). The time constant \(\tau_m\) is defined as the mean inter-update-interval that is drawn from an exponential distribution with this parameter. Using this neuron to reproduce simulations with asynchronous update 1, the time constant needs to be chosen as \(\tau_m = dt \times N\), where \(dt\) is the simulation time step and \(N\) the number of neurons in the original simulation with asynchronous update. This ensures that a neuron is updated on average every \(\tau_m\) ms. Since in the original paper 1 neurons are coupled with zero delay, this implementation follows this definition. It uses the update scheme described in 3 to maintain causality: The incoming events in time step \(t_i\) are taken into account at the beginning of the time step to calculate the gain function and to decide upon a transition. In order to obtain delayed coupling with delay \(d\), the user has to specify the delay \(d+h\) upon connection, where \(h\) is the simulation time step.

## Parameters¶

tau_m |
ms |
Membrane time constant (mean inter-update-interval) |

theta |
mV |
Threshold for sigmoidal activation function |

c_1 |
probability/ mV |
Linear gain factor |

c_2 |
probability |
Prefactor of sigmoidal gain |

c_3 |
1/mV |
Slope factor of sigmoidal gain |

Special requirements for binary neurons

As the `ginzburg_neuron`

is a binary neuron, the user must
ensure that the following requirements are observed. NEST does not
enforce them. Breaching the requirements can lead to meaningless
results.

Binary neurons must only be connected to other binary neurons.

No more than connection must be created between any pair of binary neurons. When using probabilistic connection rules, specify

`'allow_autapses': False`

to avoid accidental creation of multiple connections between a pair of neurons.Binary neurons can be driven by current-injecting devices, but

*not*by spike generators.Activity of binary neurons can only be recored using a

`spin_detector`

or`correlospinmatrix_detector`

.

## References¶

- 1(1,2,3)
Ginzburg I, Sompolinsky H (1994). Theory of correlations in stochastic neural networks. PRE 50(4) p. 3171. DOI: https://doi.org/10.1103/PhysRevE.50.3171

- 2
Hertz J, Krogh A, Palmer R (1991). Introduction to the theory of neural computation. Addison-Wesley Publishing Conmpany.

- 3
Morrison A, Diesmann M (2007). Maintaining causality in discrete time neuronal simulations. In: Lectures in Supercomputational Neuroscience, p. 267. Peter beim Graben, Changsong Zhou, Marco Thiel, Juergen Kurths (Eds.), Springer. DOI: https://doi.org/10.1007/978-3-540-73159-7_10

## Receives¶

CurrentEvent